Counting Wizards
by SerendipitousWays
Summary: Are there many wizards? (Applying logic to something to which logic need not apply should probably hurt, but we ask anyway. A thought exercise.)


**A.N.** Another thought exercise. This has math and some statistics rather than linguistics. And I got actual census information for this. I need a new hobby.

Counting Wizards

Are there very many wizards?

It's rather implied that no, there are not. After all, if there were more the names of families lost in the first war might have been forgotten by the time Harry started school, rather than getting a rambling list from Hagrid of all people: _" – the McKinnons, the Bones, the Prewitts – an' you was only a baby, an' you lived." _Hagrid, dear as he is, is not the cleverest of men, so he should give some scale: if he remembers these details off hand, what does everyone else know? And while wiping out families is always going to be a horrifying notion, in popular memory it would fade to a statistic after a decade unless it was personal.

Plus, consider that some wizarding families *cough*Black*cough* are known to practice a worrying degree of inbreeding, as well as intermarrying with other families. Sirius's parents were cousins. It's not stated, but kind of implied, that Dorea Black is James Potter's mother, making Harry part of the family… and Harry marries Ginerva Weasley, whose paternal grandmother was _also_ a Black. And I don't know offhand about the Prewitts: the degree of consanguinity could be worse. And they're related to the Longbottoms and Malfoy's and Bones and Lestranges and probably the Abbotts too (um, Neville? About Hannah…) so families regularly marry out and back in, not even just in some circles.

And then there are Rowling's various math/research fails. She has at varying points stated that:

**1)** The population of the UK's wizarding community is about **3000**. And about ten percent of the population is age 10-19, while about the same work in a bureaucratic government. So _**210**_ students (with 30 per year) and _**300**_ government workers.

**2)** But she has also said that there are about **1000** students at Hogwarts, but at the same time, which would imply about a total of _**100000**_ people and _**1000**_ government workers, _**100**_ students per year.

**3)** But Harry's year has a total of **40** students, even, which is higher than #1 gives, and goes against the whole war generation thing –there ought to be less than thirty, quite possibly by a lot due to the 'families wiped out' thing. 40 students implies _**400**_ gov workers and _**4000**_ people.

**4)** A ministry task force of **500** people built the World Cup Stadium. Did they hire out of the country? Are these non-government contractors? Because that is either half the government (2) or 200 more than the government and certainly more contractors than the country has (1) or 100 more than the government and still probably more than the country can furnish. And it took those 500 people, however they were provided, a year to build. And they must be outside hires since half to all government functions cannot stall for a year…

**5)** The Stadium holds **100000**, some of which will be tourists and visiting dignitaries and such, but a lot of whom really ought to be local. The tickets were hard to come by, and that makes it odd since even if the whole population went (1, 3) that leaves 96-97 percent of the stands to be filled by foreigners. And if the population is about 100000, most of Magical Britain should still be able to go pretty easily, provided the tickets are not too expensive. But tickets are rare. So either the population is larger (unlikely: how would you hide that many people somewhere like the UK?) or the stadium is smaller or both. Even the FIFA World Cup final match isn't always the highest drawing match of its tournament, and the average when it is is about 99400 spectators – and FIFA pulls from a much larger fan base and viewership.

So…

Let's try again.

MATHtimeMATHtime

Assuming that Magical UK and normal UK has the same population proportions…

The minimum viable population is 4169 people: this is a self sustaining population with a low level of consanguinity between pairs. (i.e. minimal inbreeding).

_MVP_=4169

The mid-year estimated population of the UK in 1991 was 50,954,800. This includes 3,056,500 youths ages 10-14 and 3,259,600 ages 15-19, which works out to 9.916% ages 11-18 for the max student population, and 8.677% for the minimum, ages 11-17. So Student Populations are:

_sPmin_=8.677%

_sPmax_=9.916%

So if the student population is 40 per year and 280 at Hogwarts and that's the whole school-going population of the country, find the total magical population:

Population (P) = 100 *280/_sP_

_Pmin_=2824

_Pmax_=3227

_Pmin _is less than _Pmax_ is less than _MVP_

Hence the inbreeding.

But it also helps explain the horror of Voldemort. If you are in a family of four, and each of your parents has a sibling married and with a child, and everyone is in a different year group, you collectively know at least 400 people: 10 family members by forty classmates, that is about fifteen percent of the entire Magical Nation! Plus if you work in offices or shops with 10 to 20 other coworkers for the adults, customers you know and like if you are in customer service, everyone's other friends, the shops you visit… And are we including grandparents? And who else are we related to? (re: inbred) Even accounting for overlap there is a guestimated average minimum of 50 extra people per person… you wipe out a family under those conditions, everyone is going to know, and what sort of terror will that instigate?

Extended family of ten, gone, and _at least_ 1 in 6 people knew one of them. That is heavy shit. That's terrifying.

And that's how Tom Riddle's army of shadows crippled Magical England.

LESSinbreedingPLEASE

But moving on. Going in reverse from the minimum viable population, what is the school age population (c)?

_c_/4169 = _sP_/100

_c_= 4169 (_sP_/100)

_cmin_ ~ 368

_cmax_ ~ 413

Or, at least 90 more students than Hogwarts canonically houses, about 13 more per year if they all attend the school.

And going with the family of four + relatives model, it does not change too much. Now 1 in 10 at least knew the deceased clan. And chances are every single person who didn't know them knows someone who did, and we are still horrified.

Now consider the perpetrators.

Why did they do this and how many are there? Even one person can do a lot of damage, but working together, and without anything to set them apart from everyone else: who can you trust? Once there is an organization in place odds are good that you know someone in it when there are only so many people to know.

BLUEbloodBLUEcollar

And the thing is, even though this is the MVP stats, in practise it is not really. Because we know that there is widespread inbreeding in this population and that cuts the viability of a large portion of that population. Add to that, these are the numbers of Hogwarts, and most Hogwarts graduates seem to go into upper level government and other specialized trades, or even estate management – not all, granted, but figure for every Hogwarts graduate that does not lead the way someone will come from elsewhere, and they will have worked harder for it.

Hogwarts is the upper crust, and the upper crust can be anywhere from 1-10% of the population.

However, I will lean towards 5-10%, as I imagine that hiding a population of 100000 or more would be perhaps overly complicated. When the minimum canon population (2824 people) is 5% the Ministry of Magic governs 56480 people, which is about as high as I would consider feasible to hide. Maybe. Any larger body of upper class would be a higher percentage.

4169 people being the upper ten gives about 42000 people total, and that's about the number I favour. There are a few thousand in every city, some go 'muggle', and hiding 1 in 1250 people shouldn't be overly complicated, especially when a significant portion never meets the world outside the magical community, and not every magical person is overtly magical. If you are barely above a squib you might never know or learn a thing.

However, 42000 gives a sustainable population that includes highly specialized trades as well as blue collar workers, those who live on the fringes of the community, the ten percent that goes into government can afford to shed people for long term projects, and there are enough people to at least start filling that damn stadium.

(And you are 400 times more likely to be a wizard than to be struck by lightning. Just saying.)


End file.
